In a theoretical, ideal, Multiple-Input Multiple-Output (MIMO) antenna system, comprising multiple transmitting antenna at a transmitter and multiple receiving antenna at a receiver, after learning the channel matrix H between the transmitter and the receiver, the transmitter decomposes the channel matrix to its singular values:H=UΛV* 
Where the ith row and jth column of H contains the flat fading channel coefficient between the ith receiver and jth transmitter antenna, and Λ is a diagonal matrix containing the singular values of H on its main diagonal. Using this decomposition, the transmitter precodes the Quadrature Amplitude Modulation (QAM symbols), {tilde over (x)} by left multiplication with the V matrix to obtain the transmitted signal x. Namely, x=V{tilde over (x)} is the signal fed to the antennas which passes through the transmission channel.
After receiving the transmitted signal, the receiver performs the post processing by left multiplication with U*, effectively creating:{tilde over (y)}==U*HV{tilde over (x)}{tilde over (y)}==U*UΛV*V{tilde over (x)}{tilde over (y)}==Λ{tilde over (x)}
Wherein, {tilde over (x)} is the data symbols, V is the pre-processing matrix obtained from the singular value decomposition (SVD) of the channel matrix, x is the vector of signals fed to the transmitter antenna, y is the column of observations at the receiver antenna, U* is the post-processing matrix based on the channel and {tilde over (y)} is the estimated data symbols that are obtained by post-processing the observations ({tilde over (y)}=Λ{tilde over (x)}).
If analog, codebook based digital or hybrid beamforming is used in a MIMO system, the pre-processing matrix V and the post-processing matrix U* can only be chosen from a set of pre-determined matrix pairs, hereinafter referred to as the matrix dictionary. Since the matrix pairs in the dictionary do not match the channel counterparts, the channel cannot be decomposed to its singular values completely and there are mismatches between the precoder/combiner and the actual transmission channel. This mismatch reduces the capacity of the MIMO channel. Furthermore, since only a finite set of known precoder/combiner matrices are used, an eavesdropper can obtain the transmitted signal correctly by brute-force searching all combiners in the set.
Accordingly, what is needed in the art is an improved system and method that increases the capacity of a MIMO transmission channel, while also providing for secrecy of the communication over the channel.
The present invention may address one or more of the problems and deficiencies of the prior art discussed above. However, it is contemplated that the invention may prove useful in addressing other problems and deficiencies in a number of technical areas. Therefore, the claimed invention should not necessarily be construed as limited to addressing any of the particular problems or deficiencies discussed herein.
All referenced publications are incorporated herein by reference in their entirety. Furthermore, where a definition or use of a term in a reference, which is incorporated by reference herein, is inconsistent or contrary to the definition of that term provided herein, the definition of that term provided herein applies and the definition of that term in the reference does not apply.
While certain aspects of conventional technologies have been discussed to facilitate disclosure of the invention, Applicants in no way disclaim these technical aspects, and it is contemplated that the claimed invention may encompass one or more of the conventional technical aspects discussed herein.
In this specification, where a document, act or item of knowledge is referred to or discussed, this reference or discussion is not an admission that the document, act or item of knowledge or any combination thereof was at the priority date, publicly available, known to the public, part of common general knowledge, or otherwise constitutes prior art under the applicable statutory provisions; or is known to be relevant to an attempt to solve any problem with which this specification is concerned.